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4. Contents Lesson 5-1Prime Factorization Lesson 5-2Greatest Common Factor Lesson 5-7Least Common Multiple

5. Lesson 1 Contents Example 1Identify Numbers as Prime or Composite Example 2Identify Numbers as Prime or Composite Example 3Find the Prime Factorization Example 4Factor an Algebraic Expression

6. Example 1-1a Determine whether the number 63 is prime or composite. Answer: The number 63 has six factors: 1, 3, 7, 9, 21, and 63. So, it is composite.

7. Example 1-1b Determine whether the number 41 is prime or composite. Answer: prime

8. Example 1-2a Determine whether the number 29 is prime or composite. Answer: The number 29 has only two factors, 1 and 29, so it is prime.

9. Example 1-2b Determine whether the number 24 is prime or composite. Answer: composite

10. Example 1-3a Find the prime factorization of 100. Method 1 Use a factor tree.

11. Example 1-3a Method 2 Divide by prime numbers. Start here. Answer: The prime factorization of 100 is

12. Example 1-3b Find the prime factorization of 72. Answer:

13. Example 1-4a ALGEBRA Factor Answer:

14. Example 1-4b ALGEBRA Factor Answer:

15. End of Lesson 1

16. Lesson 2 Contents Example 1Find the GCF by Listing Factors Example 2Find the GCF Using Prime Factors Example 3Find the GCF Using Prime Factors Example 4Find the GCF of an Algebraic Expression Example 5Use the GCF to Solve a Problem

17. Example 2-1a Find the GCF of 28 and 42. First, list the factors of 28 and 42. factors of 28: 1, 2, 4, 7, 14, 28 factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 Notice that 1, 2, 7, and 14 are common factors of 28 and 42. So, the GCF is 14.

18. Example 2-1a Check You can draw a Venn diagram to check your answer. Answer: 14

19. Example 2-1b Find the GCF of 18 and 45. Answer: 9

20. Example 2-2a Find the GCF of 20 and 32. Method 1 Write the prime factorization. The common prime factors are 2 and 2.

21. Example 2-2a Answer: The GCF of 20 and Method 2 Divide by prime numbers. Divide both 20 and 32 by 2. Then divide the quotients by 2. Start here.

22. Example 2-2b Find the GCF of 24 and 36. Answer: 12

23. Example 2-3a Find the GCF of 21, 42, and 63. Circle the common factors. The common prime factors are 3 and 7. Answer: The GCF is 3  7, or 21.

24. Example 2-3b Find the GCF of 24, 48, and 60. Answer: 12

25. Example 2-4a ALGEBRA Find the GCF of 12p 2 and 30p 3. Factor each expression. Answer: The GCF is 2 Circle the common factors.

26. Example 2-4b ALGEBRA Find the GCF of Answer: 7mn

27. Example 2-5a ART Searra wants to cut a 15-centimeter by 25-centimeter piece of tag board into squares for an art project. She does not want to waste any of the tag board and she wants the largest squares possible. What is the length of the side of the squares she should use? The largest length of side possible is the GCF of the dimensions of the tag board. The GCF of 15 and 25 is 5. Answer: Searra should use squares with sides measuring 5 centimeters.

28. Example 2-5b CANDY Alice is making candy baskets using chocolate hearts and lollipops. She has 32 chocolate hearts and 48 lollipops. She wants to have an equal number of chocolate hearts and lollipops in each basket. Find the greatest number of chocolate hearts and lollipops Alice can put in each basket. Answer: 16

29. End of Lesson 2

30. Lesson 7 Contents Example 1Find the LCM by Listing Multiples Example 2Find the LCM Using Prime Factors Example 3Find the LCM by Using Prime Factors

31. Example 7-1a Find the LCM of 4 and 6. First, list the multiples of 4 and 6. multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36... multiples of 6: 6, 12, 18, 24, 30, 36,... Notice that 12, 24,..., are common multiples. Answer: The LCM of 4 and 6 is 12.

32. Example 7-1b Find the LCM of 8 and 12. Answer: 24

33. Example 7-2a Find the LCM of 4 and 15. Write the prime factorization. The prime factors of 4 and 15 are 2, 3, and 5. Multiply the greatest power of 2, 3, and 5. Answer: The LCM of 4 and 15 is 60.

34. Example 7-2b Find the LCM of 6 and 14. Answer: 42

35. Example 7-3a Find the LCM of 18, 24, and 48. Answer: The LCM of 18, 24, and 48 is 144. LCM:

36. Example 7-3b Find the LCM of 12, 20, and 45. Answer: 180

37. End of Lesson 7

38. Online Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Mathematics: Applications and Concepts, Course 2 Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to www.msmath2.net/extra_examples.

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